- #1
probhelp150
Homework Statement
X is a Poisson Random Variable with rate of 1 per hour, following the Poisson arrival process
a. Find the probability of no arrivals during a 10 hour interval
b. Find the probability of X > 10 arrivals in 2 hours
c. Find the average interarrival time.
d. For an interval of 2 hours, let A = {10 > X > 6}, B = {5 < X < 9}, then find Pr(6 < X < 11|A, B)
e. Find E(X|A ∩ B) in the previous problem
f. If Y = exp(2X), then find E(Y |A ∪ B).
g. Find E(Y 2 |A ∪ B)
h. Find Var(Y |A ∪ B)
Homework Equations
The Attempt at a Solution
a.
##\lambda = \frac{1}{1 hour}##
##\frac{1}{1 hour} * \frac{10}{10}=\frac{10}{10 hours}##
##\lambda = 10##
##P = \frac{e^{-10}*10^x}{x!}##
b.
##\lambda = 2##
##P = \frac{e^{-2}*2^x}{x!}##
X>10 = 1 - Sum(P(0...10))
##\sum_{n=0}^{10} \frac{e^{-2}*2^x}{x!}= 0.99999##
1-0.99999=0.00001
c.
Average interarrival time = ##\frac{1}{\lambda}=\frac{1}{2}=30 minutes##
Am I doing this right so far?